Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect

The helical edge state of a quantum spin-Hall insulator can carry a supercurrent in equilibrium between two superconducting electrodes (separation L, coherence length ξ). We calculate the maximum (critical) current I(c) that can flow without dissipation along a single edge, going beyond the short-ju...

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Published inPhysical review letters Vol. 110; no. 1; p. 017003
Main Authors Beenakker, C W J, Pikulin, D I, Hyart, T, Schomerus, H, Dahlhaus, J P
Format Journal Article
LanguageEnglish
Published United States 02.01.2013
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Summary:The helical edge state of a quantum spin-Hall insulator can carry a supercurrent in equilibrium between two superconducting electrodes (separation L, coherence length ξ). We calculate the maximum (critical) current I(c) that can flow without dissipation along a single edge, going beyond the short-junction restriction L << ξ of earlier work, and find a dependence on the fermion parity of the ground state when L becomes larger than ξ. Fermion-parity conservation doubles the critical current in the low-temperature, long-junction limit, while for a short junction I(c) is the same with or without parity constraints. This provides a phase-insensitive, dc signature of the 4 π-periodic Josephson effect.
ISSN:1079-7114
DOI:10.1103/physrevlett.110.017003